基于对数正态分布理论上的小黄鱼三种资源密度估算方法比较

海洋生物的空间分布通常是不均匀的,表现为资源密度的频数分布是偏斜的,这给资源密度的估算带来一定的难度。本文基于Δ-分布模型法,结合2008年夏季、秋季和冬季东海区渔业资源底拖网大面调查中小黄鱼(Larimichthys polyactis)的渔获资料,发现三个季节小黄鱼的资源密度依次服从均值为5 068.74 g/h、73 811.34 g/h、4 282.19 g/h,标准误为2 703.61、33 522.19、1 632.95的对数正态分布。根据不同季节小黄鱼的资源密度分布特征做Monte Carlo模拟试验,利用Matlab软件随机生成12个不同的样本尺度下各1 000组资源密度值,分别计算不同样本尺度下的算术平均值、Finney-Sichel均值和几何均值,通过均方根误差(RMSE)和偏倚(BIAS)两个指标,比较三个不同的估计值与Δ-分布均值间的离散程度后发现,几何均值估算总体时的精度和准度相对较高,且随着样本尺度的增加,几何均值表现的更加稳健。特别地,几何均值受极端值影响较小。因而建议用几何均值来估算总体,来降低资源评估的误差。

Comparative study on estimating stock density of Larimichthys polyactis in the East China Sea based on lognormal theory

As the spatial distributions of marine biota are frequently patchy,samples taken from bottom trawlers exhibit a skewed distribution,which brings certain degree of difficulty in estimating the mean of stock density.Based on the data of Larimichthys polyactis collected from the bottom trawl survey conducted in the East China Sea in 2008,the estimator of the mean of stock density in summer,autumn and winter based on △-distribution were 5 068.74 g/h,73 811.34 g/h and 4 282.19 g/h,and the corresponding standard error were 2 703.61,33 522.19 and 1 632.95.From these three probability distributions of Larimichthys polyactis in different seasons,we created 1000 sets of simulated density data for each 12 samples using a pseudorandom number generator with Matlab,and calculated the arithmetic means,the Finney-Sichel estimators and the geometric means.We used the root mean squared error and deviation of the estimate from the true parameter to evaluate the performance of the estimators.The results indicated that the geometric means was advantageous,because it was relatively insensitive to extreme values in terms of accuracy and precision.At the same time,the geometric means performed better than the other two estimators when the sample sizes increased.So the geometric means was recommended to be widely used in the further study in order to reduce the estimated biomass error in fish stock assessment.